A solid glass sphere of refractive index \( n = \sqrt{3} \) and radius \( R \) contains a spherical air cavity of radius \( \dfrac{R}{2} \), as shown in the figure. A very thin glass layer is present at the point \( O \) so that the air cavity (refractive index \( n = 1 \) ) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source \( S \) emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point \( O \) and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is \( \theta \). The value of \( \sin \theta \) is__________.
